So we know that the influence function $IF$ for a functional $v$ at a point $y$ is roughly defined as: $$IF(v,F,y)=lim_{e\rightarrow 0} \frac{v(Y,G_y)-v(Y,F_y)}{e}$$ where $$G_y(y)=1(Y>y)*e + (1-e)F_y(y)$$ and $F_y$ is the CDF of y.
The question is, what is the IF for the half variance, which is defined as: $$ v_{hv}(y) = \int \left[ 1(y> E(y)(y-E(y)) \right]^2 dF_y $$
